 Static equilibrium

Static equilibrium is a state in which a mechanical system remains at rest in a specified reference frame. For a rigid body in an inertial frame, zero resultant external force and zero resultant external torque are the balance conditions:The body must also initially be at rest: zero acceleration alone does not exclude uniform translation or steady rotation.^[ref]

A free-body diagram identifies the body being analyzed and includes its external loads and support reactions. Internal action–reaction pairs cancel when both interacting parts belong to the chosen system. Choosing a different point $O$ for the torques changes their sum by a term proportional to the resultant force. Thus, when the resultant force is zero, a vanishing resultant torque about one point also vanishes about any other point.^[ref]

For an original example, take an ideal massless horizontal beam of length $4\mathrm{m}$, supported at its ends, with a downward $120\mathrm{N}$ load $1\mathrm{m}$ from the left support. Let the upward support reactions be $R_L$ and $R_R$. Vertical force balance and torque balance about the left end giveso $R_R=30\mathrm{N}$ and $R_L=90\mathrm{N}$. The nearer support carries more load because the farther reaction has the larger moment arm. Two equal and opposite forces alone would not guarantee equilibrium: a force couple can have zero resultant force and a nonzero torque.

A simple apparatus test suspends a beam from two spring balances and moves a known load along it. Account separately for the beam's own gravitational weight and its center of mass before comparing the measured reactions with the ideal calculation. The sum of the readings should track total downward load, while their difference changes with load position. Finally, static equilibrium does not imply dynamical stability: an exactly upright inverted pendulum balances at rest but departs from that state after a small disturbance.